Two angles of a triangle measure 39.5° and 61.7°. Using the Triangle Angle Sum Theorem, which states that the sum of the inside angles of all triangles must equal 180°, find the measure of the third angle. (2 points) Responses 68.8° 68.8° 78.8° 78.8° 88.8° 88.8° 98.8°

Answer 1

To find the measure of the third angle in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180°.

Let the measure of the third angle be \( x \).

We can set up the equation: \[ 39.5° + 61.7° + x = 180° \]

Now we will first add the two known angles: \[ 39.5° + 61.7° = 101.2° \]

Now, substitute this value back into the equation: \[ 101.2° + x = 180° \]

Next, to find \( x \), we can subtract 101.2° from both sides: \[ x = 180° - 101.2° = 78.8° \]

Thus, the measure of the third angle is \( 78.8° \).

The correct response is: 78.8°